L. Bell — Absolute Wave-length of Light. 365 



mate of their size as compared with those of other gratings. 

 Applying this test, the four gratings rank as follows : " 5001," 

 u 8001 L," " .2151," " 8001," where the first which gave for the 

 w. 1. 5896'14, had no sensible variation in the different orders 

 and the last, which gave 5895 - 9 7, varied in the most erratic 

 fashion. It by no means follows, however, that because a 

 grating gives identical results in the various orders, it is there- 

 fore free from errors of ruling. Witness Grating III of this 

 paper in which the error was of a kind which could not be de- 

 tected at all in the spectrometer. Yet it was large enough to 

 give, if neglected, 5896*28 for the wave-length of D r * Speak- 

 ing of errors in gratings a case in point is the work of Peirce. 

 On account of the reasons heretofore noted Peirce's standards 

 of length are somewhat uncertain in value so that no definite 

 correction can be as yet applied to his wave-length from this 

 cause. Three of his gratings, however, I have calibrated, and 

 each of them showed an error tending to diminish the wave- 

 length. If the mean result obtained from these had been 

 assumed to be correct it would have been equivalent to the 

 introduction of a constant error. Peirce's preliminary result 

 is for this reason too large by more than one part in a hundred 

 thousand ; how much more, it is impossible to say without 

 knowing the results obtained from each grating and so being 

 able to apply the corrections found. Peirce's method was 

 such as should have secured very excellent results and such 

 will undoubtedly follow a further investigation of the stan- 

 dards and gratings. Still another recent determination is that 

 by Kurlbaum, who used two good sized speculum metal grat- 

 ings and measured them with particular care. Like the previ- 

 ous experimenters he neglected, although he did not ignore, 

 the errors of ruling and consequently the results he obtained 

 are somewhat in doubt. A serious objection, moreover, to his 

 work is the very small spectrometer he used. To undertake a 

 determination of absolute -wave-length with a spectrometer 

 reading by verniers to 10" only, and furnished with telescopes 

 of only one inch aperture is simply courting constant errors. 

 More especialty is this true since it would be hard to devise a 

 method more effective in introducing the errors of ruling, 

 than to use a grating with telescopes too small to utilize its 

 full aperture, and then determine the grating space by meas- 

 uring the total length of the ruled surface. Kurlbaum's grat- 

 ings, too, were of an unfortunate size, 42 and 43 mm broad 

 respectively, and consequently by no means easy to measure. 

 On the whole his result, 5895*90 is not surprising. 



*The results given by the gratings used by the author, neglecting the correc- 

 tion A would be as follows : 



I, 5896-20; II, 589614; III, 5896'28 ; IV, 5896-12 

 Curiously enough the mean would be practically unchanged. 



